A radio broadcasts at a wavelength of 3.06 m. Near the broadcast tower the electric-field ampli

step 1 So the frequency F is the speed of the wave that is C upon the wavelength lambda. And from this,

A radio broadcasts at a wavelength of 3.06 m. Near the...

A radio broadcasts at a wavelength of $3.06 \mathrm{~m}$. Near the broadcast tower the electric-field amplitude is $2700 \mathrm{~N} / \mathrm{C}$. Calculate (a) the frequency, (b) the wave number, and (c) the magnetic-field amplitude of the electromagnetic wave.

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Key Concepts

Electromagnetic Waves

Electromagnetic waves are disturbances in the electromagnetic field that propagate through space, carrying energy. They consist of oscillating electric and magnetic fields which are perpendicular to each other and to the direction of wave propagation. Their behavior is described by Maxwell's equations.

Speed-Wavelength-Frequency Relationship

This concept is based on the equation c = ?f, where c is the speed of light, ? is the wavelength, and f is the frequency. It provides the fundamental connection between how long each wave cycle is (wavelength) and how many cycles occur per second (frequency) in a propagating wave.

Wave Number

The wave number is defined as k = 2?/?, representing the spatial frequency of a wave. It quantifies the number of radians per unit distance and helps describe the oscillatory nature of waves in space.

Electric and Magnetic Field Relationship

In free space, the amplitudes of the electric and magnetic fields in an electromagnetic wave are linked by the speed of light, with the relation B = E/c. This shows that the magnetic field amplitude is directly proportional to the electric field amplitude, scaled by the reciprocal of the speed of light.

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